Yes it is perfectly normal for some seedlings to have purple, or red, or green, and brown stems too and sometimes, all these colours!
At this stage your seedling is living and growing from the contents of the embryo, so it is impossible to have any sort of deficiency at this stage.
"Over watering" can not cause purple stems and seedlings actually need moist conditions for root growth and under watering will retard root growth.
Think what happens in nature - when it rains, water doesn't just fall next to the stem of a plant, does it? No, of course not, the whole area is wet and so should your pot be after watering, an even moistness from edge of the pot to other edge of the pot and deeply too. As long as you don't saturate your pots, your seedling will be fine, just use common sense and think about "what would happen in nature" and base your judgement on this. Cannabis has been relying on those principles for Eons and is not a dinky dainty precious princess that needs to be treated as though it is so fragile that looking at it strangely may be enough to "upset" it. Trust me, I have been growing for 35+ years and cannabis is a remarkably resilient plant that can handle all sorts of adversity and is not a plant that needs to be molly coddled or wrapped in cotton wool.
Have a look at my diary "cannabis conundrums" and in week 7 you will find pictures of a 3 week old seedling with its roots exposed, and this may give you an idea as to why giving adequate water with deep penetration is vital for seedling/plant growth. Whatever you do, do not water with a syringe, spray bottle or shot glass, this is entirely useless. Your plant at this size may not need large amounts of water for general health, but it does need an evenly moist substrate, from top to bottom and side to side for roots to be able to grow and explore unhindered. Watering with a syringe/spray bottle/shot glass will give enough water so that your plant doesn't die, but it will not encourage a healthy root system to form. After all, the plant is relying on a healthy root system for productive above ground growth.
If seedlings/plants were so sensitive to "too much" water, how would anyone ever grow plants in hydro, deep water culture or aeroponics, were the roots are always in liquid or "excess moisture" their whole lives? Just remember - moist not wet - and everything is going to be OK.
Hope this helps,..... Organoman.